The present invention relates to portfolio risk management, and more particularly to calculating the Conditional Value-at-Risk (CVaR), a widely used risk measure, for a portfolio.
One of the main objectives of portfolio risk management is to evaluate and improve the performance of the portfolio while reducing exposure to a financial loss. A financial portfolio refers to a collection of investments owned by an individual or an organization. An investment includes, but is not limited to, a stock, a bond, a currency, a derivative, a mutual fund, a hedge fund, cash equivalents, etc. A risk refers to a likelihood of losing investment values in a portfolio. Estimating the risk of a portfolio through a simulation (e.g., Monte Carlo simulation or any other equivalent simulation), is a fundamental task in portfolio risk management. Different measures of risk call for different simulation techniques.
A standard benchmark for a measurement of a risk is “Value-at-Risk” (VaR). For a given confidence level β(0<β<1, typical β=95%), the β-level VaR is the loss in the portfolio's value that is exceeded with the probability 1−β. However, as a risk measure, VaR lacks coherency in the sense that it does not necessarily encourage diversification. This is because the VaR value of a combination of two portfolios can be greater than the sum of VaR values of the individual portfolios. Philippe Artzner, et al. “Coherent Measure of Risk,” Mathematical Finance, vol. 9, no. 3, July 1999, pp. 203-228, wholly incorporated by reference, describes VaR in detail.
An alternative risk measure to VaR is “Conditional Value-at-Risk” (CVaR), which is also known as “Average Value-at-Risk”, “Mean Excess Loss”, “Mean Shortfall” or “Tail VaR”. For a given level β, the β-level CVaR value is the conditional expectation of the loss above the β-level VaR value. The value of CVaR is always greater than or equal to that of the corresponding VaR. CVaR can be calculated by generating random samples to simulation losses of a portfolio, and then averaging those samples that are greater than the VaR value.